Comparative Analysis of Nuclear Matrix Elements of 0νβ+β+ Decay and Muon Capture in 106Cd

Comparative analyses of the nuclear matrix elements (NMEs) related to the $0\nu\beta^+\beta^+$ decay of $^{106}$Cd to the ground state of $^{106}$Pd and the ordinary muon capture (OMC) in $^{106}$Cd are performed. This is the first time the OMC NMEs are studied for a nucleus decaying via positron-emitting/electron-capture modes of double beta decay. All the calculations are based on the proton-neutron quasiparticle random-phase approximation with large no-core single-particle bases and realistic two-nucleon interactions. The effect of the particle-particle interaction parameter $g_{\rm pp}$ of pnQRPA on the NMEs is discussed. In the case of the OMC, the effect of different bound-muon wave functions is studied.